Question: Simplify the following expression: $ z = \dfrac{-9t}{t + 6} - \dfrac{-6}{5} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{-9t}{t + 6} \times \dfrac{5}{5} = \dfrac{-45t}{5t + 30} $ Multiply the second expression by $\dfrac{t + 6}{t + 6}$ $ \dfrac{-6}{5} \times \dfrac{t + 6}{t + 6} = \dfrac{-6t - 36}{5t + 30} $ Therefore $ z = \dfrac{-45t}{5t + 30} - \dfrac{-6t - 36}{5t + 30} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{-45t - (-6t - 36) }{5t + 30} $ Distribute the negative sign: $z = \dfrac{-45t + 6t + 36}{5t + 30}$ $z = \dfrac{-39t + 36}{5t + 30}$